This is, in fact, the case. There is an apparent general "contraction" or abandonment of Roman urban centers in Britain in the last quarter of the 4th century CE. We see buildings being abandoned, not repaired, or, in some cases, being treated as "shells" for smaller timber structures within. This is a general trend across multiple sites. These buildings are also not replaced elsewhere nearby, at least not as far as we know. The interpretation of the evidence is then that these places are no longer being occupied, or are being occupied in a very different way.

The 5th century CE represents something of a "gap" in occupation, and our knowledge about occupation. There have been attempts to "connect" late Romano-British occupation with the Anglo-Saxon occupation that comes next, but for right now there is a bit of a gap there, in the 5th century mostly, and we can't quite make them meet. There are a few scattered places where one can find Anglo-Saxon material in the same place as late Romano-British material, but this is quite rare and we are talking about individual finds of objects in most cases. The largest site for this is Canterbury, where there is some kind of Romano-British occupation into the 5th century, though greatly reduced and quite different than what came before, and also at roughly the same time the very earliest indications of Grubenhäuser "pit houses." There is similar at Colchester. In both cases, I believe, the pit houses were dug into earlier levels, and so could have post-dated the earlier levels by several decades. From London is a famous Anglo-Saxon disc brooch from a Late Roman bath house, but it was found in the collapsed rubble of the building.

But in all these cases, even if we can establish that early Anglo-Saxons were there, they do not continue there. All the other evidence indicates that the largest centers (London, Colchester, Winchester, Canterbury) were abandoned from the early or mid-5th century and nothing detectable was going on there again until the 7th century CE at the earliest, and in some cases later. And this is the case for dozens, if not hundreds, of smaller urban and rural Romano-British sites throughout Britain.

I won't summarize it all here, but A.S. Esmonde Cleary has a lengthy discussion of this topic in The Ending of Roman Britain (Routledge 1989/2005), especially Chapter Six.

The answer depends on the definition of "London" in OP's question. The main settlement area of Early Medieval Lundenwic was in fact a little (about a mile) down to the old center of Roman Londinium. These two settlement areas would merge into one big city in Late Anglo-Saxon period at first.

While more can always be said, I hope the following posts by /u/BRIStoneman will be suffice to grasp the basic surrounding of early medieval London:

• The Museum of London states that Lundenwic was founded by the Anglo-Saxons in 600AD to the west of the Roman City, which had been abandoned since the early 5th century. Why did the Anglo Saxons not simply reoccupy the old walled city?
• Is it a coincidence that Roman London came to become the capital of England , or did the romans make London into a large and power city ?

Recommended Reading:

• Naismyth, Rory. Citadel of the Saxons: The Rise of early London. London: I. B. Tauris, 2019.